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| Авторизация |
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| Lewis J.D. — CRM Monograph Series, vol.10: A Survey of the Hodge Conjecture |
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| Предметный указатель |
Canonical bundle for complete intersections 42
Canonical bundle for hypersurfaces 42
Canonical bundle for projective space 41
Canonical bundle of Grassmannian 54
Canonical divisor 214
Canonical extension 235 242
Cartan decomposition 303 315
Cartan involution 303 315
Cartan involution, differential 303
Cartan structure equation 104
Cartier divisor 48
Cauchy — Riemann equations 1
Cech cohomology 43 44
Cellular decompositiom 7 13
ch(V), (Chern character) 119
CH*(X) (Chow group) 181
Character group 318
Chemistry 336
Chern character 119
Chern class 106 110 112 119
Chern class for dual bundle 107
Chern class of line bundle 33 46
Chern class, functoriality 108
Chern class, total Chern class 106
Chern root 119
Chow group 181
Chow group of projective space 255
Chow group, continuous part 173 181
Chow group, finite dimensional 272
Chow group, finite dimensionality 251 261
Chow group, higher 291
Chow group, infinite dimensionality 261
Chow group, level 272 277
Chow variety of zero-cycles 248 249
Chow’s Lemma 287
Chow’s Moving Lemma 181
Chow’s theorem 11 110
Chronological listing 350
Classical group 300
Clifford algebra 303
Clifford algebra, even 303
CM-field 309 332 337 342
CM-Hodge cycle 341
CM-type 90 94 307 309 315—318 320 326 329—331 333 337 338 340—344 35O
CM-type, degenerate 338—340
CM-type, degenerate in composite dimension 339
CM-type, index of degeneracy 335
CM-type, lower bound 341
CM-type, nondegenerate 316 326 338
CM-type, primitive 340
CM-type, rank 337 339
CM-type, simple 338 339 341
Coboundary, Cech 44
Cocycle, Cech 44
Coherent sheaf 9
Cohomology of blow-up 198
Cohomology of complex tori 12
Cohomology of Grassmannian 12
Cohomology of projective space 8
Cohomology,  349
Cohomology, Cech 43
Cohomology, de Rham 31
Cohomology, Dolbeault 31
Cohomology, etale 348
Cohomology, primitive 123 128 134 193 211
Cohomology, singular 58
Complete intersection 43 92 119 254 259
Complex Abelian variety 305 313 316
Complex Abelian variety, isogenous 306
Complex linear map 1
Complex structure 305 314
Complex torus 3 305
Complex torus, polarization 306
Condition ( ) 336
Connected linear algebraic group 312
Connected linear group 302
Connection 103
Connection matrix 103
Connection, canonical 106
Connection, Gauss — Manin 233
Connection, metric 106
Cotangent bundle 18
Cremona transformation 27
Cubic threefold, Hodge conjecture 209
Cubic threefold, Jacobi inversion 200
Curvature form 33
Curvature matrix 104
Curve 3
Cusp 9
Cycle class map 273
Cycles algebraically equivalent 180
Cycles rationally equivalent 180
Cylinder homomorphism 204 223 279
D 30
De Rham cohomology 31
de Rham cohomology, finite dimensionality 145
de Rham cohomology, isomorphism theorem 38 46 60 145
deg Z (degree) 270
Degenerate 338 340 341
Degree of a curve 67
Degree of a divisor 63
Degree of a hypersurface 11 43
Dehn twist 73
Derivation 302
Derivation, left invariant 302
Derived group 347
Desingularization 4 61 200
Determinant cycle 335
df 30
Differential 29 302
Dihedral group 338
dim X (dimension) 8
Dimension of a variety 8 11
Dimension of a variety, infinite dimensionality 252
Dirichlet inner product 151
Dirichlet norm 151
Div(X) (divisor group on X) 48
Divisibility (of A*(X)) 182
Division algebra 307
Division quaternion algebra 307
Division quaternion algebra, indefinite 309
Divisor 43 318 335
Divisor, Cartier 48
Divisor, effective 43
Divisor, exceptional 21
Divisor, line bundle associated to 49
Divisor, linear equivalence 49
Divisor, principal 49
Divisor, rational equivalence 49
Divisor, Well 48
Dolbeault cohomology 31
Dolbeault cohomology, finite dimensionality 145
Dolbeault cohomology, isomorphism theorem 38
Dolbeault lemma 31
Double point, ordinary 71 80
Dual bundle 18
Dual bundle, Chern class 107
Dual map for hypersurfaces 80
Dual projective space 23 52
Dual variety 53 81
Effective divisor 43
Effective zero-cycle 248
Elliptic curve 4 307 329 330 342
Elliptic curve of CM-type 89 318
Elliptic curve, product 317
Elliptic integral 5
End(A) (endomorphism ring of Abelian variety A) 306
Endomorphism algebra 324
Euler characteristic 119 193
Ex(n) (a set of integers) 344
| Exceptional cycle 324 334 338
Exceptional cycle in codimension 2 334
f* (pull-back) 172
Fano variety of k-planes 218
Fano variety of lines 201
Fermat curve 320 341
Fermat hypersurface 11
Fermat threefold, Hodge conjecture 94
Fiat vector bundle 208 233 242
Filtration 265
Filtration by coniveau 272
Filtration by niveau 285
Filtration on Chow group 265
Filtration on Chow group, Bloch — Beilinson 273 281
Filtration on Chow group, Murre’s approach 280
Filtration, arithmetic 87 260
Filtration, Hodge 85 88 234 241 284 292
Filtration, monodromy weight 242
Filtration, weight 241 284 292
Fine sheaf 37
Flag manifold 91 259
Flag space 103 112
Frame 19
Fubini — Study metric 33
Fundamental 2-form of a metric 32
Fundamental class 61 68 237 285
G(n,k) (Grassmannian) 12
Galois group 340
Garding inequality 151 153
Gauss — Manin connection 233
General linear group 328 332
Genus 3
Genus, geometric 41
Genus, topological 120
Geometric genus 41
Geometric genus of complete intersection 50
Geometric genus of hypersurface 50
GHC(p,l,X) (general Hodge conjecture) 88
GL(n) (general linear group of invertible matrix  ) 299
Goursat’s lemma 316 319 330
Grassmannian 12
Grassmannian, canonical bundle 54
Grassmannian, cohomology 12
Grassmannian, tangent bundle 54
Green’s operator 144 152
Griffiths group 186 238
Griffiths group, non-triviality 84 238
Grothendieck’s counterexample 88
Group homomorphism, equivariant 300
Group homomorphism, linear 300
GSp(2n) (symplectic similitude group in 2n variables) 301
GSp(V,E) (symplectic similitude group) 301
Gysin map 134
Gysin sequence 86
Gysin sequence, associated to a blow-up 198 222
Harmonic 141 142
Harmonic form 144
Hermitian form 301 322 327 328 341 348
Hermitian manifold 24
Hermitian metric 24
Hermitian symmetric domain 335 336
Hermitian type 303 314
hessian 81
Hg(A) (Hodge group of Abelian variety A) 312
Hg(V) (Hodge group of rational Hodge structure V) 312
Hilbert scheme 99 186 227
Hirzebruch — Riemann — Roch theorem 119
Hirzebruch — Riemann — Roch theorem for curves 120
Hirzebruch — Riemann — Roch theorem for surfaces 120
Hirzebruch — Riemann — Roch theorem, generalization 121
Hodge (p,q) decomposition theorem 57 161
Hodge class 322
Hodge class, exceptional 93 322—324 332 334
Hodge conjecture 313 321 333 349
Hodge conjecture for Abelian varieties 93 297—351
Hodge conjecture for complete intersections 92
Hodge conjecture for flag manifolds 91
Hodge conjecture for hypersurfaces 92
Hodge conjecture for singular varieties 287
Hodge conjecture for unirational varieties 92
Hodge conjecture for uniruled varieties 92
Hodge conjecture, counterexample 66
Hodge conjecture, general 342—345 347 348
Hodge conjecture, general, Grothendieck amended 88
Hodge conjecture, popular version 64 88
Hodge cycle 313 318 322 333 341 342
Hodge cycle, determinant 335
Hodge cycle, exceptional 333 334
Hodge decomposition 57 85 161 310 328
Hodge filtration 85 234 241 284 292 310 342
Hodge filtration, rational 88 261
Hodge group 312—317 321 326 328 330 332 337 344 347 349
Hodge group, semisimplicity 314 336 347
Hodge inner product 140
Hodge manifold 12
Hodge number 85 119
Hodge ring 321
Hodge structure 85 313 323
Hodge structure, morphism 313
Hodge structure, rational 310—312 314 342 343 345
Hodge structure, rational, associated to an Abelian variety 311
Hodge structure, rational, dual 311
Hodge structure, rational, morphism 311
Hodge structure, rational, Mumford — Tate group 312
Hodge structure, rational, polarization 311 313
Hodge structure, rational, type 311
Hodge structure, real 310
Hodge theorem 144
Hodge type, family of Abelian varieties 347 349 350
Hodge vector 311 313
Hodge — Kaeihler identities 160
Hodge — Riemann bilinear relation 167
Homological equivalence 84 180 194 273
Homological equivalence vs. algebraic equivalence 84 173
Homological equivalence vs. numerical equivalence 274
Homology see also “cohomology”
Homology class 77
Homology, Borel — Moore 68 284
Homology, primitive 74 228
Hopf manifold 13 34
Hopf manifold, not Kaehler 13
Horizontal displacement 205
Horizontal normal function 240
Horizontality condition 235
HRR (Hirzebruch — Riemann — Roch theorem) 119
Hyperelliptic curve 321
Hyperelliptic curve, Jacobian 319
Hyperelliptic Riemann surface 7
Hyperplane at infinity 7 76 192
Hyperplane bundle 22
Hypersurface 8 11
Imaginary quadratic field 324 326 328
Indecomposable 320
Infinitesimal period relation 234 240
Integral homology 14
Intersection pairing 61
Invariant cycles conjecture 349 350
Invariant theory 337
Irreducible subset 8
Irregularity 83
J (endomorphism defining a complex structure) 305
Jacobi identity 301
Jacobi inversion 75 173 238
Jacobi inversion, failure 79 187 238
Jacobian 292 320
Jacobian of a curve 75
Jacobian of a Fermat curve 319
Jacobian of elliptic modular curves 330
Jacobian of hyperelliptic curve 321
Jacobian, generalized 75
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